1. Suppose you are in the market for a new home and are interested in a new housing community under construction in a different city.
a) The sales representative informs you that there are two floor plans still available, and that there are a total of 115 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation.
X + Y = 115
b) The sales representative later indicates that the number of homes available with the floor plan #2 is 4 times the number of houses with floor plan #1. Write an equation that illustrates this situation. Use the same variables you used in part a.
Y=4X
c) Use the equations from part A and part B of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available (find x and y). Describe the steps you used to solve the problem.
X+4X=115
5X=115
115/5=23 houses with plan #1 and Y=4(23) Y=92 houses in plan #2
2. As you are leaving the community, you notice another new community just down the street. Because you are in the area, you decide to inquire about it.
a) The sales representative here tells you they also have two floor plans available, but they only have 54 homes available. Write an equation that illustrates the situation. Use x and y to denote floor plan #1 and floor plan #2 respectively.
X+Y=54 or Y=(54-x)with the substitution.
b) The representative tells you that floor plan #1 sells for $180,000 and floor plan #2 sells for $250,000. She also mentions that all the available houses combined are worth $11,400,000. Write an equation that illustrates this situation. Use the same variables you used in part A.
180,000x+250,000y=11,400,000
c) Use elimination to determine how many houses with each floor plan are available. Explain how you arrived at your answer.
Substitute (54-x) for y, find x
180,000x + 250,000(54-x)=11,400,000
180,000x + 1,350,0000- 250,000 = 11,400,000
180,000x – 250,000=11,400,000-1,350,000
70,000x= 10,050,000
X=
3. You recently started the paperwork to purchase your new home, and you were just notified that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifters and Quick Move, to discuss their rates. Heavy Lifters charges a fixed $100 fee plus $45 per hour. Quick Move charges $85 per hour with no additional fees.
a) Which mover provides a better deal for 2 hours of work? How did you arrive at your answer?
b) Which mover provides a better deal for 5 hours of work? How did you arrive at your answer?
a) To determine which mover provides a better deal for 2 hours of work, we need to calculate the total cost from each mover and compare them.
For Heavy Lifters:
Fixed fee = $100
Hourly rate = $45
Total cost = Fixed fee + (Hourly rate × Number of hours)
Total cost = $100 + ($45 × 2)
Total cost = $100 + $90
Total cost = $190
For Quick Move:
Hourly rate = $85
Total cost = Hourly rate × Number of hours
Total cost = $85 × 2
Total cost = $170
Comparing the total costs, we can see that Quick Move provides a better deal for 2 hours of work as their total cost is $170, which is lower than the $190 cost from Heavy Lifters.
b) To determine which mover provides a better deal for 5 hours of work, we follow the same calculation process.
For Heavy Lifters:
Total cost = $100 + ($45 × 5)
Total cost = $100 + $225
Total cost = $325
For Quick Move:
Total cost = $85 × 5
Total cost = $425
Comparing the total costs, we can see that Heavy Lifters provides a better deal for 5 hours of work as their total cost is $325, which is lower than the $425 cost from Quick Move.